Category: Integration

Question Number 139432 by normabaru last updated on 27/Apr/21 Answered by Jme Eduardo last updated on 27/Apr/21 $$\left({a}\right)\:\:{if}\:\:{x}={t}^{\mathrm{2}} \:\:{and}\:\:{y}={t} \\ $$$$ \\ $$$$\underset{{t}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\left[\frac{\mathrm{2}{t}^{\mathrm{4}} }{{t}^{\mathrm{4}}…

Question Number 139427 by Fikret last updated on 26/Apr/21 $$\underset{\:\sqrt{\mathrm{2}}} {\overset{\mathrm{3}\sqrt{\mathrm{2}}} {\int}}\sqrt{{x}^{\mathrm{2}} −\mathrm{2}}{dx}+\underset{\mathrm{0}} {\overset{\mathrm{4}} {\int}}\sqrt{{x}^{\mathrm{2}} +\mathrm{2}}{dx}\:=? \\ $$ Answered by MJS_new last updated on 27/Apr/21…

Question Number 8296 by tawakalitu last updated on 06/Oct/16 $$\mathrm{Give}\:\mathrm{the}\:\mathrm{integral}\:\mathrm{representation}\:\mathrm{of}\:\:\mathrm{2333}! \\ $$ Commented by 123456 last updated on 07/Oct/16 $${n}!=\underset{\mathrm{0}} {\overset{+\infty} {\int}}{t}^{{n}} {e}^{−{t}} {dt} \\…

Question Number 8281 by tawakalitu last updated on 06/Oct/16 $$\int\frac{\mathrm{6}\:\mathrm{sinx}\:\mathrm{cosx}}{\mathrm{sinx}\:+\:\mathrm{cosx}}\:\mathrm{dx} \\ $$ Answered by Yozzias last updated on 06/Oct/16 $$\frac{\mathrm{sinx}}{\mathrm{sinx}+\mathrm{cosx}}=\mathrm{1}−\frac{\mathrm{cosx}}{\mathrm{sinx}+\mathrm{cosx}} \\ $$$$\therefore\:\mathrm{I}=\int\frac{\mathrm{sinxcosx}}{\mathrm{sinx}+\mathrm{cosx}}\mathrm{dx}=\int\left(\mathrm{1}−\frac{\mathrm{cosx}}{\mathrm{sinx}+\mathrm{cosx}}\right)\mathrm{cosxdx} \\ $$$$=\int\left(\mathrm{cosx}−\frac{\mathrm{cos}^{\mathrm{2}} \mathrm{x}}{\mathrm{sinx}+\mathrm{cosx}}\right)\mathrm{dx}…

Question Number 73751 by ~blr237~ last updated on 15/Nov/19 $${Find}\:\:{out}\:{the}\:{value}\:{of}\:\:\: \\ $$$$\:\:{J}=\int_{\mathrm{0}} ^{\infty} \int_{\mathrm{0}} ^{\mathrm{1}} \left(\mathrm{2}{e}^{−\mathrm{2}{xy}} −{e}^{−{xy}} \right){dxdy}\: \\ $$ Commented by mathmax by abdo…